Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2201.02116 · Physical Review A

Nonclassicality criteria for N -dimensional optical fields detected by quadratic detectors

Jan Peřina, Pavel Pavlíček, Václav Michálek, Radek Machulka, Ondřej Haderka

Published Jan 10, 2022• 6 citations
arXivHTMLPDF

Abstract

Nonclassicality criteria for general $N$-dimensional optical fields are derived. They involve intensity moments, the probabilities of photon-number distributions, or combinations of both. The Hillery criteria for the sums of the probabilities of even or odd photon numbers are generalized to $N$-dimensional fields. As an example, the derived nonclassicality criteria are applied to an experimental three-mode optical field containing two types of photon-pair contributions. The accompanying nonclassicality depths are used to mutually compare their performance.

DOI
10.1103/physreva.105.013706

Related papers

Nonclassicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors. II. Criteria based on probabilities

Jan Peřina, Ondřej Haderka, Václav Michálek

Numerous nonclassicality criteria based on the probabilities of experimental photocount or theoretical photon-number distributions are derived using several approaches. Relations among the derived criteria are revealed and the fundamental criteria are identified. They are grouped into parametric systems that allow the analysis of the nonclassicality from different points of view (``local'' nonclassicality, pairwise character of photon correlations, etc.). Considering their structure, the criteria may be divided into groups that differ in the power to resolve the nonclassicality. Quantification of the nonclassicality using the Lee nonclassicality depth and the nonclassicality counting parameter is discussed. The number of field modes used is identified as an important parameter that may cause unexpected results. An appropriate linear transformation of a photocount (photon-number) distribution into its $s$-ordered form, needed for the determination of the nonclassicality depth, is derived. For comparison, the derived criteria are applied both to an experimental photocount histogram of a twin beam and the reconstructed photon-number distributions with different levels of the noise.

arXiv:2010.06927•Physical Review A•Oct 20, 2020•18 citations

Nonclassicality and entanglement criteria for bipartite optical fields characterized by quadratic detectors

Jan Peřina, Ievgen I. Arkhipov, Václav Michálek +1 more

Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, nonnegative polynomials, the matrix approach, and the Cauchy-Schwarz inequality. Different approaches for deriving these inequalities are compared. Using the experimental photocount histogram generated by a weak noisy twin beam monitored by a photon-number-resolving intensified CCD camera, the performance of the derived inequalities is compared. A basic set of 10 inequalities suitable for monitoring entanglement of a twin beam is suggested. Inequalities involving moments of photocounts (photon numbers) as well as some containing directly the elements of photocount (photon-number) distributions are also discussed as a tool for revealing nonclassicality.

arXiv:1710.03793•Physical Review A•Oct 18, 2017•34 citations

Non-classicality of optical fields as observed in photocount and photon-number distributions

Jan Peřina, Václav Michálek, Ondřej Haderka

Non-classicality criteria for optical fields based on the probabilities of photocount and photon-number distributions are derived. Relations among the criteria obtained by the applied methods are revealed. Redundant criteria are identified. The performance of the fundamental criteria is tested on a set of potentially sub-Poissonian fields generated by photon-number-resolved post-selection from a mesoscopic twin beam. The corresponding non-classicality depths are determined to quantitatively compare the used criteria.

Optics Express•Oct 6, 2020•9 citations

Experimental detection of nonclassicality of single-mode fields via intensity moments

Ievgen I. Arkhipov, Jan Peřina, Ondřej Haderka +1 more

Nonclassicality criteria based on intensity moments and derived from the usual matrix approach are compared to those provided by the majorization theory. The majorization theory is shown to give a greater number of more suitable nonclassicality criteria. Fifteen experimentally useful criteria of the majorization theory containing the intensity moments up to the fifth order are identified. Their performance is experimentally demonstrated on the set of eleven potentially nonclassical states generated from a twin beam by postselection based on detecting a given number of photocounts in one arm by using an iCCD camera.

arXiv:1612.04434•Optics Express•Dec 12, 2016•16 citations

Higher-order sub-Poissonian-like nonclassical fields: Theoretical and experimental comparison

Jan Peřina, Václav Michálek, Ondřej Haderka

Criteria defining higher-order sub-Poissonian-like fields are given using five different quantities: moments of (I) integrated intensity, (II) photon number, (III) integrated-intensity fluctuation, (IV) photon-number fluctuation, and (V) elements of photocount and photon-number distributions. Relations among the moment criteria are revealed. Performance of the criteria is experimentally investigated using a set of potentially sub-Poissonian fields obtained by post-selection from a twin beam. The criteria based on moments of integrated intensity and photon number and those using the elements of photocount distribution are found as the most powerful. States nonclassical up to the fifth order are experimentally reached in the former case, even the ninth-order nonclassicality is observed in the latter case.

arXiv:1709.08406•Physical Review A•Sep 28, 2017•37 citations

Hierarchy of feasible nonclassicality criteria for sources of photons

Radim Filip, Lukáš Lachman

We present an ab-initio derivation of a hierarchy of efficient nonclassicality criteria for sources of photons. The operational criteria are explicitly proposed for the linear optical multiport and feasible multiplexed single-photon detectors. The lowest criterion is equivalent to the frequently used ${g}^{(2)}(0)$ autocorrelation measurement testing the anticorrelation effect of photons. We also derive a hierarchy of criteria for the detectors capable to at least partially estimate photon-number distribution. We prove the usefulness of both hierarchies to detect the nonclassical states from the noisy multimode single-photon sources and the nonclassical states from the multiphoton sources.

Physical Review A•Oct 15, 2013•30 citations
Nonclassicality criteria for general NNN-dimensional optical fields are derived. They involve intensity moments, the probabilities of photon-number distributions, or combinations of both. The Hillery criteria for the sums of the probabilities of even or odd photon numbers are generalized to NNN-dimensional fields. As an example, the derived nonclassicality criteria are applied to an experimental three-mode optical field containing two types of photon-pair contributions. The accompanying nonclassicality depths are used to mutually compare their performance.
Numerous nonclassicality criteria based on the probabilities of experimental photocount or theoretical photon-number distributions are derived using several approaches. Relations among the derived criteria are revealed and the fundamental criteria are identified. They are grouped into parametric systems that allow the analysis of the nonclassicality from different points of view (``local'' nonclassicality, pairwise character of photon correlations, etc.). Considering their structure, the criteria may be divided into groups that differ in the power to resolve the nonclassicality. Quantification of the nonclassicality using the Lee nonclassicality depth and the nonclassicality counting parameter is discussed. The number of field modes used is identified as an important parameter that may cause unexpected results. An appropriate linear transformation of a photocount (photon-number) distribution into its sss-ordered form, needed for the determination of the nonclassicality depth, is derived. For comparison, the derived criteria are applied both to an experimental photocount histogram of a twin beam and the reconstructed photon-number distributions with different levels of the noise.
Numerous inequalities involving moments of integrated intensities and revealing nonclassicality and entanglement in bipartite optical fields are derived using the majorization theory, nonnegative polynomials, the matrix approach, and the Cauchy-Schwarz inequality. Different approaches for deriving these inequalities are compared. Using the experimental photocount histogram generated by a weak noisy twin beam monitored by a photon-number-resolving intensified CCD camera, the performance of the derived inequalities is compared. A basic set of 10 inequalities suitable for monitoring entanglement of a twin beam is suggested. Inequalities involving moments of photocounts (photon numbers) as well as some containing directly the elements of photocount (photon-number) distributions are also discussed as a tool for revealing nonclassicality.
Non-classicality criteria for optical fields based on the probabilities of photocount and photon-number distributions are derived. Relations among the criteria obtained by the applied methods are revealed. Redundant criteria are identified. The performance of the fundamental criteria is tested on a set of potentially sub-Poissonian fields generated by photon-number-resolved post-selection from a mesoscopic twin beam. The corresponding non-classicality depths are determined to quantitatively compare the used criteria.
Nonclassicality criteria based on intensity moments and derived from the usual matrix approach are compared to those provided by the majorization theory. The majorization theory is shown to give a greater number of more suitable nonclassicality criteria. Fifteen experimentally useful criteria of the majorization theory containing the intensity moments up to the fifth order are identified. Their performance is experimentally demonstrated on the set of eleven potentially nonclassical states generated from a twin beam by postselection based on detecting a given number of photocounts in one arm by using an iCCD camera.
Criteria defining higher-order sub-Poissonian-like fields are given using five different quantities: moments of (I) integrated intensity, (II) photon number, (III) integrated-intensity fluctuation, (IV) photon-number fluctuation, and (V) elements of photocount and photon-number distributions. Relations among the moment criteria are revealed. Performance of the criteria is experimentally investigated using a set of potentially sub-Poissonian fields obtained by post-selection from a twin beam. The criteria based on moments of integrated intensity and photon number and those using the elements of photocount distribution are found as the most powerful. States nonclassical up to the fifth order are experimentally reached in the former case, even the ninth-order nonclassicality is observed in the latter case.
We present an ab-initio derivation of a hierarchy of efficient nonclassicality criteria for sources of photons. The operational criteria are explicitly proposed for the linear optical multiport and feasible multiplexed single-photon detectors. The lowest criterion is equivalent to the frequently used g(2)(0){g}^{(2)}(0)g(2)(0) autocorrelation measurement testing the anticorrelation effect of photons. We also derive a hierarchy of criteria for the detectors capable to at least partially estimate photon-number distribution. We prove the usefulness of both hierarchies to detect the nonclassical states from the noisy multimode single-photon sources and the nonclassical states from the multiphoton sources.